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Poisson Transforms for Line Bundles from the Shilov Boundary to Bounded Symmetric Domains

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Lie Groups: Structure, Actions, and Representations

Part of the book series: Progress in Mathematics ((PM,volume 306))

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Abstract

For homogeneous line bundles over a bounded symmetric domain all Poisson transforms coming from line bundles over the Shilov boundary are determined and explicit Poisson kernels are given in terms of natural trivializations. The eigenvalues of the Casimir operator are computed. Generalized Hua-type equations for the Poisson transforms are described.

To Joe Wolf on his 75t h birthday

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Acknowledgements

This paper is partially supported by the NSF and by a PSC-CUNY grant.

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Authors and Affiliations

  1. Mathematics Department, H.H. Lehman College, City University of New York, Bronx, NY, 10468, USA

    Adam Korányi

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  1. Adam Korányi
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Correspondence to Adam Korányi .

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Editors and Affiliations

  1. Remagen, Germany

    Alan Huckleberry

  2. Jacobs University School of Engineering and Science, Bremen, Germany

    Ivan Penkov

  3. Yale University Dept. Mathematics, New Haven, Connecticut, USA

    Gregg Zuckerman

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Korányi, A. (2013). Poisson Transforms for Line Bundles from the Shilov Boundary to Bounded Symmetric Domains. In: Huckleberry, A., Penkov, I., Zuckerman, G. (eds) Lie Groups: Structure, Actions, and Representations. Progress in Mathematics, vol 306. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7193-6_7

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